{"paper":{"title":"Regularity of solutions to degenerate $p$-Laplacian equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"David Cruz-Uribe, Kabe Moen, Virginia Naibo","submitted_at":"2011-10-14T18:44:56Z","abstract_excerpt":"We prove regularity results for solutions of the equation \\[div(< AXu,X u>^{(p-2)/2} AX u) = 0,\\] $1<p<\\infty$, where $X=(X_1,...,X_m)$ is a family of vector fields satisfying H\\\"ormander's ellipticity condition, $A$ is an $m\\times m$ symmetric matrix that satisfies degenerate ellipticity conditions. If the degeneracy is of the form \\[\\lambda w(x)^{2/p}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq \\Lambda w(x)^{2/p}|\\xi|^2,\\] $w \\in A_p$, then we show that solutions are locally H\\\"older continuous. If the degeneracy is of the form \\[ k(x)^{-2/p'}|\\xi|^2\\leq < A(x)\\xi,\\xi>\\leq k(x)^{2/p}|\\xi|^2, \\] $k\\in A_{p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3295","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}